A Analysis Of Equilibrium Solution Of Two Ecology-epidemic Models With Diffusion

For the implementation of biological control with the interaction among differentinteractions, the effection of the diffusion on the steady states of several prey-predatormodels is discussed.A prey-predator model with the Holling IItype functional responses and thehomogeneous Neumann boundary condition is developed; the existence of non-constantpositive steady state is obtained by using the topological degree theory.A prey-predator model with the Holling IIItype functional responses andself-diffusion is considered, under the homogeneous Neumann boundary condition, inthe first place, the stability of the constant positive steady state of the model is provedby using linearing and considering Lyapunov function; and then, we discuss thecondition of non-existence of non-constant positive steady state of the correspondingsteady state problem in considering the diffusion alone by using energy method andthe topological degree.